(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f:R^{nxn}-->R^{nxn}be defined by f(A) = A^{2}. Prove that f is differentiable. Find the derivative of f.

2. Relevant equations

f(a + h) = f(a) + f'(a)h + [itex]\phi[/itex](h)

3. The attempt at a solution

f(A + H) = (A + H)^{2}= A^{2}+ AH + HA + H^{2}

f(A) is given by A^{2}. So the sum of the derivative operator and the remainder term is AH + HA + H^{2}. The problem is that I don't know how to determine which terms are part of the derivative.

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# Real analysis question

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